scholarly journals A note on exponentially harmonic morphisms

2000 ◽  
Vol 42 (1) ◽  
pp. 25-29 ◽  
Author(s):  
Eric Loubeau ◽  
Stefano Montaldo

We prove that exponentially harmonic morphisms are precisely the Riemannian submersions with minimal fibres.1991 Mathematics Subject Classification 58E20.

2001 ◽  
Vol 44 (1) ◽  
pp. 71-85 ◽  
Author(s):  
Paul Baird

AbstractA harmonic morphism defined on $\mathbb{R}^3$ with values in a Riemann surface is characterized in terms of a complex analytic curve in the complex surface of straight lines. We show how, to a certain family of complex curves, the singular set of the corresponding harmonic morphism has an isolated component consisting of a continuously embedded knot.AMS 2000 Mathematics subject classification: Primary 57M25. Secondary 57M12; 58E20


2009 ◽  
Vol 40 (4) ◽  
pp. 377-382 ◽  
Author(s):  
Bang-Yen Chen ◽  
Shihshu Walter Wei

By studying cohomology classes that are related with $p$-harmonic morphisms, we extend some previous results of the first author on Riemannian submersions with minimal fibers to $n$-harmonic morphisms which are submersions.


1993 ◽  
Vol 36 (1) ◽  
pp. 133-143 ◽  
Author(s):  
Sigmundur Gudmundsson

Let M and N be simply connected space forms, and U an open and connected subset of M. Further let π: U → N be a horizontally homothetic harmonic morphism. In this paper we show that if π has totally geodesic fibres and integrable horizontal distribution, then the horizontal foliation of U is totally umbilic and isoparametric. This leads to a classification of such maps. We also show that horizontally homothetic harmonic morphisms of codimension one are either Riemannian submersions modulo a constant, or up to isometrics of M and N one of six well known examples.


2004 ◽  
Vol 06 (03) ◽  
pp. 419-430 ◽  
Author(s):  
M. T. MUSTAFA

The structure of local and global harmonic morphisms between Riemannian manifolds, with totally fibres, is investigated. It is shown that non-positive curvature of the domain obstructs the existence of global harmonic morphisms with totally geodesic fibres and the only such maps from compact Riemannian manifolds of non-positive curvature are, up to a homothety, totally geodesic Riemannian submersions. Similar results are obtained for local harmonic morphisms with totally geodesic fibres from open subsets of non-negatively curved compact and non-compact manifolds. During the course, we prove non-existence of submersive harmonic morphisms with totally geodesic fibres from some important domains, for instance from compact locally symmetric spaces of non-compact type and open subsets of symmetric spaces of compact type.


Author(s):  
Ümit Totur

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0


2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomoya Miura ◽  
Shun Maeta

Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.


2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Aaron Frederick Bulagang ◽  
James Mountstephens ◽  
Jason Teo

Abstract Background Emotion prediction is a method that recognizes the human emotion derived from the subject’s psychological data. The problem in question is the limited use of heart rate (HR) as the prediction feature through the use of common classifiers such as Support Vector Machine (SVM), K-Nearest Neighbor (KNN) and Random Forest (RF) in emotion prediction. This paper aims to investigate whether HR signals can be utilized to classify four-class emotions using the emotion model from Russell’s in a virtual reality (VR) environment using machine learning. Method An experiment was conducted using the Empatica E4 wristband to acquire the participant’s HR, a VR headset as the display device for participants to view the 360° emotional videos, and the Empatica E4 real-time application was used during the experiment to extract and process the participant's recorded heart rate. Findings For intra-subject classification, all three classifiers SVM, KNN, and RF achieved 100% as the highest accuracy while inter-subject classification achieved 46.7% for SVM, 42.9% for KNN and 43.3% for RF. Conclusion The results demonstrate the potential of SVM, KNN and RF classifiers to classify HR as a feature to be used in emotion prediction in four distinct emotion classes in a virtual reality environment. The potential applications include interactive gaming, affective entertainment, and VR health rehabilitation.


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